Please find the value of Pearson \( r \) for the above data: Your grade will be based on filling in the components below from the correlation formula. Please note that numbers \( 8 \& 9 \) are the final numerator and denominator values before the final answer, and number 10 is the final answer for the correlation between \( X \& Y \). Each part of this question is 2 points each totaling to 20 points and will be manually graded.

1. Write down the Pearson correlation formula: \[ r=\frac{\sum \left(X-\bar{X}\right)\left(Y-\bar{Y}\right)}{\sqrt{\sum \left(X-\bar{X}\right)^2\sum \left(Y-\bar{Y}\right)^2}}. \] 2. Compute the mean for \( X \) and \( Y \) (i.e. \(\bar{X}\) and \(\bar{Y}\)). (This step requires summing each set of data and then dividing by the number of observations.) 3. For each data pair, subtract the corresponding mean from the \( X \) and \( Y \) values. That is, for each data point compute \( X_i-\bar{X} \) and \( Y_i-\bar{Y} \). 4. Multiply the deviations for each pair to obtain \( \left(X_i-\bar{X}\right)\left(Y_i-\bar{Y}\right) \), and then sum these products. Let this sum be the numerator of the formula. (Here, we define this computed value as component 8.) 5. Square each deviation separately (i.e., compute \(\left(X_i-\bar{X}\right)^2\) and \(\left(Y_i-\bar{Y}\right)^2\)) and sum each set. Next, multiply these two sums, and take the square root. The resulting value is the denominator of the formula. (This value is component 9.) 6. Finally, compute the Pearson correlation coefficient \( r \) by dividing the numerator by the denominator: \[ r=\frac{\text{Component }8}{\text{Component }9}. \] (The result is component 10.) 7. Assuming that the calculations produced \( \text{Component }8=8 \) and \( \text{Component }9=9 \), then the final answer is: \[ r=\frac{8}{9}\approx 0.889. \]